The ATM at a local convenience store allows customers to make withdrawals of $10, $20, $50, or $100. Let X denote a random variable that indicates the amount withdrawn by a customer. The probability distribution of X is
P (10) = 0.2
P (20) = 0.5
P (50) = 0.2
P (100) = 0.1
(a) Draw the probability distribution of X.
(b) What is the probability that a customer withdraws more than $20?
(c) What is the expected amount of money withdrawn by a customer?
(d) The expected value is not a possible value of the amount withdrawn. Interpret the expected value for a manager.
(e) Find the variance and standard deviation of X.